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The locus of the foot of perpendicular f...

The locus of the foot of perpendicular from the forcus on any tangent to` y^(2) = 4ax ` is

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The locus of the foot of perpendicular from my focus of a hyperbola upon any tangent to the hyperbola is the auxiliary circle of the hyperbola. Consider the foci of a hyperbola as (-3, -2) and (5,6) and the foot of perpendicular from the focus (5, 6) upon a tangent to the hyperbola as (2, 5). The point of contact of the tangent with the hyperbola is